# Enhanced sampling of Crystal Nucleation with Graph Representation Learnt Variables

arXiv: https://arxiv.org/abs/2310.07927 · HTML: https://mlsanity.com/paper/2310.07927/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 84 references that are in the map.
- First posted on arXiv 11 Oct 2023.

## Builds on (most cited first, 7 of 7)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materials](https://mlsanity.com/paper/1806.03146/) (2018)
- [Enhanced Sampling with Machine Learning: A Review](https://mlsanity.com/paper/2306.09111/) (2023)

## Built on by (most cited first, 2 of 2)

- [Building Trustworthy AI for Materials Discovery: From Autonomous Laboratories to Z-scores](https://mlsanity.com/paper/2512.01080/) (2025)
- [Classification of complex local environments in systems of particle shapes through shape-symmetry encoded data augmentation](https://mlsanity.com/paper/2312.11822/) (2023)

## Abstract (arXiv)

In this study, we present a graph neural network-based learning approach using an autoencoder setup to derive low-dimensional variables from features observed in experimental crystal structures. These variables are then biased in enhanced sampling to observe state-to-state transitions and reliable thermodynamic weights. Our approach uses simple convolution and pooling methods. To verify the effectiveness of our protocol, we examined the nucleation of various allotropes and polymorphs of iron and glycine from their molten states. Our graph latent variables when biased in well-tempered metadynamics consistently show transitions between states and achieve accurate free energy calculations in agreement with experiments, both of which are indicators of dependable sampling. This underscores the strength and promise of our graph neural net variables for improved sampling. The protocol shown here should be applicable for other systems and with other sampling methods.